"How often have I said to you that when you have eliminated the
impossible, whatever remains, however improbable, must be the truth?" (Sir
Arthur Conan Doyle).

The Torah, like the Freudian dream, has always been believed by
some of its interpreters to have a latent content in addition to its
manifest content. Throughout many generations, mystics devoted great
efforts to discovering what they thought were divine secrets or messages
encoded in the Torah. In 1994, Statistical Science, a peer reviewed
journal of the American Institute of Mathematical Statistics, published
what appeared to be statistical proof, based on a scientific experiment,
that the bible contains a hidden code, in the form of words spelled by
equal-sized letter skips (ELS, for short).1

Here is an example of an ELS: In the book of Genesis, the first
appearance of (the Hebrew letter corresponding to) T is followed 50
letters later by an O, which is followed 50 letters later by R, and yet
another 50 letters later by H, thus spelling the word TORH (which in
Hebrew has just these four letters).

This curious anecdotal discovery is one of several that were made
a few decades ago by the Slovakian Rabbi Weissmandel. Apparently, no
similar discoveries were made until the 1980s, when some people realized
they could search the Torah for meaningful ELSs much more effectively with
the aid of computers. Computers allowed reliable counts of skips much
larger than 50 -- 500, 1000, 5000, etc., thereby expanding the scope of
the search beyond ordinary human capacity.

Around 1984, Doron Witztum, an Orthodox Jew from Jerusalem,
conceived the idea of writing the entire book of Genesis as a single
extended page consisting only of letters (deleting punctuation marks and
closing up spaces). This huge rectangle of letters could have any width
one likes. For example, since Genesis consists of about 78,000 letters,
it can be written as a page of 78 rows, each 1000 letters wide, or as a
page of 780 rows, each 100 letters wide, etc. ELSs cn be read
horizontally, vertically, or diagonally, and in any direction: left to
right or right to left, top down or bottom up.

An example in an English text is shown in Figure 1, which is a piece
of a huge page on which the entire text of Moby Dick was written. It
displays various words relating to the assassination of Martin Luther King
written as ELSs (e.g., MLKING, TENN, GUN). In this case, the size of skip
between adjacent rows is over 26,000 letters (since that is exactly the
width of the full page).

Figure 1. Martin Luther King was fatally shot

in Tennessee on April 4,1968. 2

Playing around with his computer, and using the book of Genesis as
his text, Witztum noticed that sometimes thematically related words (e.g.
"HAMMER" and "ANVIL") both appeared as ELSs within the same small letter
array -- as in Figure 1. Other times, an ELS seemed to be related to an
ordinary word sequence in the text in a striking way, as is also shown in
Figure 1.

A much trumpeted later example is Figure 2, taken from the jacket
of a 1997 best-selling book by Michael Drosnin. 3 The text in the rows is
from the Pentateuch (the books of Numbers and Deuteronomy). The eight
letters in the column spell "Yitzhak Rabin". They are separated from each
other by almost 5000 letters in the original text. Rabin's name
intersects a string of words which Drosnin (who doesn't speak Hebrew)
translated as "an assassin who will assassinate" (the Jerusalem Bible
translates these words as: "a man ... who had killed"). This letter
array was found by Drosnin in 1994, a full year before Israel's Prime
Minister Rabin was assassinated. He was sufficiently impressed by his own
discovery to try to bring it to the attention of Israeli security forces
and Rabin himself. When Rabin was assassinated a year later, an
impressive centerpiece for Drosnin's book had been established.

By now Witztum had teamed up with Ilya Rips, another Orthodox Jew
and a professor of mathematics at The Hebrew University. Rips realized
that in a sufficiently large text interesting patterns of ELSs can be
found in proximity as the result of mere chance. After all, there is a
large number of possibilities to exploit: What words to search for, where
to start the search, how many letters to skip, etc. Convinced nonetheless
that something extraordinary was happening in the book of Genesis, he
sought to subject his hunch to a systematic quantitative test.

For their test, Rips and Witztum wanted a list of related word
pairs, constructed according to objective, well-defined criteria. They
decided on a list of famous Jewish rabbis, along with their dates of death
or birth. They drew the rabbis from an encyclopedia which gives brief
biographical sketches of Jewish rabbis who lived between the 9th and 18th
century AD. 4 To be included, the rabbis had to have a sufficiently long
entry (over 3 columns of text for the first list, over 1.5 columns of text
for a later list) and a date of death. A computer program searched
Genesis for ELSs corresponding to the names of the rabbis and their dates
of death (in Hebrew, dates are written with letters only, requiring no
digits). Where the search was successful (some names and some dats were
not found as ELSs at all), the program also measured how "close" a rabbi's
ELS name was to his ELS date.

The rabbis' names and their respective dates did not form any neat
or regular pattern in Genesis. Readers who can verify on their own,
without needing a computer, how TORH is spelled out as an ELS in the
opening phrases of Genesis, cannot, practically speaking, see for
themselves how close the rabbis names and dates are found in Genesis.
Even with the aid of a computer, a rabbi's name and his date are rarely
both found in the kind of small letter array shown in Figures 1 and 2.
Moreover, most names of rabbis are closer to some other rabbi's date than
to their own. In fact, the measurement of distance between names and
dates was so complicated and unintuitive, that only statistical analysis
could determine whether they really were closer to each other than could
be expected by chance.

Witztum and Rips were not statisticians, and their early attempts
at such analysis were fraught with errors. They ended up following a
suggestion of Prof. Persi Diaconis of Harvard, which we shall not describe
here. The analysis very strongly indicated that whatever was going on
could hardly be attributed to mere chance. If what Witztum and Rips
found was not due to chance, it can only be described as a miracle,
because the rabbis lived millenia later than the time the Torah was
written. Since they could not have been deliberately coded into the text
by an ancient scribe, the code could only be the work of a clairvoyant,
presumably divine, intelligence.

The study, which came to be known as The Famous Rabbis Experiment,
was carried out between 1986 and 1988. It took until 1994 for the results
to be published in Statistical Science. In the eyes of many, the Torah
Codes had graduated from the realm of esoteria, populatd by the likes of
tea-leaf reading, to the hallowed halls of Science.

What could have moved a statistical journal to even review, let
alone publish, such an outlandish experiment, in which even the
then-editor, Prof. Robert Kass of Carnegie-Mellon, put no credence? The
answer, as is often the case, lies in the human element more than in the
experiment itself.

Ilya Rips, a soft-spoken cherubic man sporting the long white
beard and black skullcap worn by Ultra Orthodox Jews, was born in the
USSR. In 1969, when he was a young secular Communist of about 20, he made
headline news by setting himself on fire in the Riga town square, in
protest of the Russian invasion of Czechoslovakia. He was put in a mental
institution for three years, and then allowed to emmigrate to Israel,
where he acquired both a doctorate in mathematics, and a new identity as
an Orthodox Jew. His unworldliness is exemplified in the following story:
In 1973, during Israel's Yom Kippur War, Rips volunteered to pump gas in a
gas station which was short of manpower, due to the mobilizatin of all
reserve soldiers. Long after the war had ended, he was still pumping gas
voluntarily, to the owner's delight. To friends trying to persuade him to
resume his own life he said that the landlord had not released him yet.
Only when someone argued that Rips was taking the job from someone who
needed it for his living did Rips leave the gas station.

Doron Witztum has an MSc in Physics from The Hebrew University,
acquired before his conversion to Orthodoxy, but has never held an
academic position. But for about 15 years he has devoted much of his time
to Codes research. Oft heard claims that he holds an academic position
are untrue. There is a third author, Yoav Rosenberg, then a young student
who helped with the programming, and has avoided the limelight. Drosnin,
and the media, largely credit Rips with discovering the codes. Rips'
reputation lends more credibility to the codes than the unknown Witztum
could have ever mustered alone. However, Rips himself credits the codes
to Witztum, who is also listed first of the three authors of their joint
paper, in spite of conventions favoring alphabetical ordering of authors.

When Rips and Witztum made their Torah Codes discoveries, Rips
described them to colleagues at The Hebrew University. One, Robert
Aumann, a well known game-theorist and also an Orthodox Jew, took a
particular interest in the work. He played a prominent role in bringing
it to the attention of the scientific community. Being more fluent in
English than Witztum and Rips, he rewrote their research report, turning
it into the dry, tight, and lucid version that was later published in
Statistical Science (and is reproduced in full in The Bible Code). He
also arranged for Rips to give a public lecture in the Israeli Academy of
Sciences, an event that caused much embarassment and furor in the Academy.
Perhaps most significantly, Aumann, also a member of the American National
Academy of Sciences, attempted to have the paper published in the
prestigious journal of the Academy, the PNAS. This journal will only
publish a paper that is sponsored by an Academy member. Aumann was
willing to sponsor the paper, and sent it for peer review to a bevy of
world reknowned statisticians, among them Harvard's Persi Diaconis.

Diaconis was a perfect choice for the job. As well as being a
MacArthur Prize winner for his work in mathematics and statistics, he is
also a first class magician and an expert on how statistics is used -- or
rather, misused -- in support of ESP research, and other fantastical
claims. Diaconis had been introduced to Torah Codes research earlier by
his Harvard Math Department colleague, David Kazhdan, an old friend of
Rips' from their early years in Russia, who, like Rips, had also become an
Orthodox Jew. When Diaconis was first approached, only the first list of
rabbis existed. Diaconis had suggested that a fresh sample be
constructed, and this is what prompted the second list of rabbis mentioned
above. Diaconis also suggested a different and ingenious way of
calculating the statistical significance of Witztum and Rips's results.
He was quite sure that the results of the famous rabbis experiment
wouldn't survive the statistical significance test, and wouldn't be
repeated in the new sample.

Being a magician, Diaconis should have known better. His own
audiences also often believe that they can uncover his tricks, only to be
even further baffled when the tricks survive the scrutiny and suspicions.
How Diaconis was foiled will be described later. But, being a
statistician as well as a magician, he knew that the implications of the
experiment depended more on the integrity of the researchers, than on the
reported numbers. A clever and unscrupulous researcher can manipulate the
numbers. Again and again Diaconis asked: Are these people reliable, are
they honest? Again and again he was assured of the absolute integrity of
Rips. No one he asked, however, could vouch for Witztum.

Impressed by the evidence, but quite unconvinced of the existence
of the codes, Diaconis ultimately recommended against publication of the
work in the PNAS, much to Aumann's chagrin. However, he assisted in
getting the paper published in Statistical Science, hoping that this
"would give statisticians a chance to say out loud what they thought was
wrong" with it. As we shall see later on, figuring out what was wrong
with it, and especially being able to prove it, only happened several
years later.

It is appropriate to remark here that -- contrary to common lay
perceptions -- the decision to publish a scientific paper is by no means
an endorsement of its findings or conclusions. Some philosophers of
science, most notably the late Karl Popper, even argue that science
progresses strictly by refutation: conclusions and results are meant to
be refuted. Aumann's anger at Diaconis was not for refusing to believe
Rips and Wiztum's results, but only for refusing to recommend their
publication in the PNAS. Moreover, though Aumann has been this work's
most ardent advocate in the academic world, he claims that he himself is
still not convinced of the existence of codes. He is only convinced that
the case for codes is strong. Both Aumann and Diaconis believed that even
if the results were flawed, the flaws had a better chance of being exposed
after publication, simply because they would draw more and wider
attention. Indeed, according to the Treasurer of the Institute of
Mathematical Statistics, the journal issue in which the codes paper was
published is far and away the best-selling issue Statistical Science ever
published.

But although Statstical Science, in its own words, offered the
paper to its readers "as a challenging puzzle", for several years, the
paper elicited no critical response. Apparently, readers who assumed
that there was something wrong with the results, couldn't be bothered to
take the time to figure out what it was. Those who didn't personally know
Rips were probably not even much intrigued. Three years were to pass
before the puzzle was tackled.

While Torah Codes research was being largely ignored by
scientists, it was warmly embraced by a quite different group, Jewish
proselytizers. Judaism does not encourage missionary attempts to recruit
non-Jews. The Talmud states that "... the proselytes are as burdensome to
Israel as leprosy". 5 But in Israel, in the US, and in other countries,
there are many outreach seminars and other forums intended to convert
secular, non-believing Jews into Orthodoxy (both Rips and Witztum are such
born again Jews). Aish Ha'Torah ("The flame of the Torah") is a
Jerusalem-based group that operates "Discovery seminars", designed to
encourage such conversions by a "rationalistic" approach. The Torah Codes
are the jewel in the crown of their seminars, offered as objective,
scientific proof that the Torah is of divine origin, and targeted
primarily at educated, sophisticated Jews who respect numbers, science,
and rational thinking. According to an article in The Wall Street
Journal, in 1996 alone, "about 240 Jewish community centers, schools and
synagogues [in the US] eager to expand their membership - have paid Aish
Ha'Torah ... about $1000 to put on each Discovery seminar. Aish HaTorah
... has put about 60,000 people worldwide through the seminar since 1987 -
more than one-third of those just in the past two
years". 6

The apparent seal of approval conferred by the publication in
Statistical Science played an essential role in this use of Codes
research, as did the Foreword to a book which Doron Witztum had
self-published in Hebrew a few years earlier, 7 which was signed by four
prominent mathematicians: Furstenberg, of The Hebrew University, I.
Piatetski-Shapiro of Yale, and D. Kazhdan and J. Bernstein, of Harvard.
Although the Foreword only said that the work was "serious" and
"sufficiently striking to deserve a wide audience", many saw it as an
endorsement by the most respectable and knowledgeable authorities. These
authorities all happen to be Orthodox Jews, and personally familiar with
Rips.

Their sentiment, however, is hardly widely shared. The very quest
for objective proof of the divine origin of the Torah or for the existence
of God is anathema to many Orthodox Jews, who regard belief as necessarily
a pure act of faith. The triviality and puerileness of the codes
increases these people's disdain for the attempts to prove their
existence. An outspoken voice in this camp is that of Shlomo Sternberg,
who in addition to being a professor of mathematics at Harvard is also an
ordained Orthodox rabbi. He has written that the very notion of the codes
research is a disgrace for Judaism, as well as for mathematics. Prof.
Barry Simon, the Orthodox Jewish chairperson of Caltech's Math Department,
has gone so far as to draw up a formal statement, that can only be signed
by professional mathematicians and statisticians, attesting to the flaws
and follies of the famous rabbis experiment. Scores have signed it.
The network of personal contacts between various mathematicians in
Israel and in the US has drawn into the fray a sizable number of
mathematicians. Many are from the previous USSR. Many are Orthodox.
Personal friendships have been forged around the codes. Others have
foundered.

Another concerned group consists of some Israeli Orthodox rabbis
who were debating the value of Codes research, and its possible religious
and theological significance. They had reason for concern. Some time
ago, several hundreds of thousands Israelis received in the mail a little
black book published by the Christian Mission, which makes extensive use
of Torah Codes to prove that Jesus is the Messiah (for example, in Numbers
chapter 21 verse 10, where instructions are given to the priests who
sacrifice the sacrificial lambs, taking every third letter from the first
H on spells "Hence the blood of Jesus", an expression which in the
vowelless Hebrew takes up three words totalling eight letters). 8
However, outside of some religious circles and a small circle of people
around Rips and Witztum, codes research was still a completely marginal
and esoteric phenomenon.

And then came Drosnin's book. On May 29, 1997, Simon and Schuster
took out a full page ad in The New York Times announcing its debut, with
the following caption: "In all of history, few books have completely
changed the way we view the world. The Bible was one. The Bible Code is
another". Within a week, the book had been featured in all seriousness on
CNN, The New York Times, TIME magazine, and Newsweek (in the Religion
section). In short order, it was featured in other leading newspapers, in
the Today Show, the Oprah Show, etc. . It went into translation, and
topped bestseller lists all over the world. A year later it was released
with renewed fanfare in paperback. A 1999 movie, The Omega Code, is
predicated on the existence of the codes, and plays primarily to Christian
audiences. On the other hand, Harvard, by awarding Drosnin its annual
Ignobel prize in literature for 1997, interjected a rare note of humor.

In a nutshell, the book tells of how Drosnin, a journalist and
writer, had met with Rips and learned about the Torah Codes and how to
look for ELSs. It shows a great many letter arrays he found, in which
various ELSs are highlighted for the reader's benefit. Drosnin's arrays
resemble those in Witztum's earlier book. The boldest departure between
the books is in Drosnin's attempt to read into his letter arrays
predictions of the future. His only "success" (he admits to some
failures) is the "prediction" of Rabin's assassination, verfiably found
before the assassination actually occurred. How impressive is this
prediction?

The skeptic may note the following: 1. The possibility of an
attempt on Rabin's life was not only raised by many at the time, but was
actually promoted by some extremist rightwing circles. 2. Drosnin's memo
to Israel's chief scientist at the Israeli Ministry of Defense stated: "I
think Rabin is in real danger, but that the danger can be averted" (p.
187). This much, however, was not only a common concern, but would have
been confirmed whether Rabin had been assassinated or not. 3. That the
ELS for "Yitzhak Rabin" crossed the words (under the Drosnin's dubious
translation) "assassin who will assassinate" no more predicts that Rabin
will be assassinated than that Rabin himself will assassinate. Moreover,
there is no indication which Yitzhak Rabin is referred to (this is a not
uncommon name in Israel). As with the Delphic Oracle, the interpretation
of the Bible Code depends on what the interpreter wants it to. The
success of Drosnin's prediction is only in the eyes of the beholder.

More impressive by far is the fact that Drosnin has made much more
money and fame out of the Torah Codes than all codes researchers put
together ever have. Not surprisingly, there are suits pending against
him, for example, for failing to credit the writers of the software he
used to look for codes). Also impressive is Drosnin's unique position in
simultaneously claiming to believe in Codes -- but not in God.

In spite of this success, or perhaps because of it, Rips and
Witztum have made public statements to the press repudiating the book and
distancing themselves from it -- an oddity in itself, considering that The
Bible Code extols and extends their work. Drosnin's book, much more than
the Statistical Science paper, let the Bible Codes genie out of the
bottle, and brought it to the world's attention.

Creative magicians love to amaze and baffle their peers with a new
trick they've invented, challenging them to figure out the secret of the
trick on their own. An important psychological element in this task is
strict adherence to what you know with certainty to be impossible.
Suppose you see a magician cutting the pretty lady in two, separating her
smiling face, upper torso and all, from her twitching toes, long-booted
legs and all, and then putting them together again. It is wrong to ask:
"How can the lady be cut in half and glued back together again?", because
the obvious answer to that question is: She cannot! But you are on your
way if you ask: "How can one appear to be cutting the lady in half and
then putting her together again?".

The codes research raises the obvious question: "How could the
names of rabbis and their dates of death have been encoded in a text
written millenia before the rabbis were even born?" For the skeptic, this
is the wrong question. Compelling evidence that such a code truly exists
is the stuff of The X-Files. A committed skeptic does not ask how the
Codes got into the Torah, but rather how did they appear to get there.
Interestingly, this should be the question even for those who literally
believe that the Torah was dictated by God letter for letter on Mt. Sinai,
because there is little disagreement among biblical scholars that the many
different texts of the Torah that we have today differ much more from the
original text of antiquity than they do from each other -- which is by
quite a lot. Witztum and Rips ignore the problem of conducting research
on an artificial publisher's version called the Koren edition, which is
known to be hundreds if not thousands of letters different than the
original of antiquity. Drosnin falsely claims that "every Hebrew Bible
that now exists is the same letter for letter", and that the text used for
the codes research "has not changed in at least a thousand years" (p. 38).
In any case, it had two thousand years to change before this millenium.
And it did.

We ourselves became interested in the codes after attending a
colloquium at The Hebrew University's Center for the Study of Rationality,
in which Aumann presented the work of Witztum and Rips (oddly, Witztum and
Rips presence in the audience was unacknowledged). At that talk, as at
others, a common reaction was: "How does the list of rabbis fare in
other books?". In fact, Witztum and Rips had tried out their list on
several other texts, among them, at some referee's suggestion, War and
Peace (in the Hebrew translation). 9 In the parlance of methodology,
these texts serve as a kind of "control" against the possibility that some
result that appears unique or remarkable actually might crop up anywhere.
But just as Witztum and Rips hoped, the rabbis list did not fare well on
any of these texts. Genesis was clearly special.

Recall that in addition to checking other texts, Witztum and Rips
were also asked by Diaconis to check another list. This is called in the
parlance of methodology replication, or cross-validation. Notably, though
Witztum and Rips seemed willing to check a large number of control texts,
they were only willing to perform a single replication. That replication
was the second list of rabbis mentioned earlier. The usual function of
replication is to demonstrate an effect's reliability, stability, or
generalizability. But where "miracles" are involved, replication serves
another purpose: it subtly guards against methodological or other
wrongdoing, in a manner we shall elucidate.

Without having said so in so many words, Diaconis, Kass, and other
skeptics, clearly suspected that in spite of Witztum and Rips'
self-declared goal of "uniformity and objectivity with regard to the
choice of the pairs" (p. 431), indispensable in so delicate an inquiry,
they had perhaps -- deliberately or inadvertently -- drawn the target only
after shooting the arrow, so to speak. In other words, they may have had
some advance knowledge of some rabbis whose names were close to their
dates, and used that knowledge to construct the rules for drawing their
lists.

Checking a new list according to the same rules or protocol which
governed the first list can be viewed as tantamount to removing the first
arrow, and requiring the authors to shoot a fresh arrow into the same
target, with no opportunity for adapting its position. That is why
Diaconis insisted on a fresh sample. Witztum and Rips were well aware of
the suspicions regarding their experimental procedure. Their paper
states: "In order to avoid any conceivable appearance of having fit the
tests to the data, it was later decided to use a fresh sample, without
changing anything else [e.g., the distance measurement, the spelling
rules, etc.]" (p. 43, our emphasis).

When the second list proved as successful as the first, the
referees were stumped. Short of saying: "We simply don't believe it",
the referees had taken their mandate as far they could. Referees are not,
nor are they meant to be, detectives. Their job is to evaluate a
manuscript on the presumption that it is truthful, and to check its
theoretical and methodological integrity -- not its veracity. In an
interview given in 1995, Kass said: "I don't think anyone ended up
believing it. They still think there's some kind of flaw, but they don't
know what it is". 10 The flaw turned out to be that the target had after
all been drawn around the arrow in the second list too. Later analysis
revealed statistical traces of how this legerdemain feat was achieved. We
shall outline this analysis.

A close look at the list of famous rabbis suggests where
"uniformity and objectivity" had been departed from, and where "fitting
the tests to the data" might have occurred, even in the second list.
Readers may be forgiven for assuming hitherto that each rabbi in the lists
was represented by a single name and a single date, perhaps forgetting for
a moment that a person's "name" or even a person's "date of death" is not
a unique and well-defined sequence of letters. Say one is born on July 4.
Should the letter sequence one looks for be: JULY4 (recall that 4 in
Hebrew is represented by a letter)? or JULY4TH? how about 4THOFJULY? Is
the name of the present American president Bill Clinton? Mr. Clinton?
Mr. President? Or just Clinton? Bill?

It seems that Witztum and Rips could have elected to do one of two
things: use a single, predefined, way of writing dates -- e.g., just
JULY4TH, and a single predefined way of writing names -- e.g., just first
initial and family name (BCLINTON). They chose not to do that. Or they
could have used all possible ways of writing names and dates. This is
problematic. Regarding dates, do "all possible ways" include
"AMERICANINDEPENDENCEDAY"? Regarding names, note that at birth, Mr.
Clinton's first intial was not B, and his family name was not Clinton --
he was named William Jefferson Blythe IV. How does one define "all names"
-- and how does one verfiy that a list is complete? Witztum and Rips' odd
solution to this crucial matter was to fail to acknowledge it as a
problem. They used some, but not all, names, and some, but not all, date
forms. Later -- but not in the paper -- they stated that the choices
were made by experts they had consulted, according to apriori rules. In
the opinion of other experts, however, their list is "arbitrary",
"unscientific", even "appalling".

To give an example of one of many inconsistent choices, suppose
some name has become accepted as the family name of a rabbi even though he
did not use it himself. Should it be used? In the case of one rabbi,
the name Emden was included, even though it had been explicitly disowned
by that rabbi. Yet in the case of another rabbi, the name Chelma, long
accepted as his family name, was rejected on the grounds that it was no so
used in the life-time of that rabbi.

Most important for assessing the statistical claims, however, is
not so much the quality of the list as its flexibility. The very
possibility of selecting what to include in it and what not allows, if not
fitting the tests to the data, then fitting the data to the tests.
Indeed, in a September 1997 interview with The Jerusalem Report,
Furstenberg (the author of the Foreword to Witztum's book) conceded that
"Five years ago, [the experiment] looked fairly foolproof. You put the
data in the computer and it comes up with remarkable results. But there
was a greater choice of names than one realized. I would now be more
hesitant to write even that quasi-endorsement which appeared in Witztum's
book" (p. 18). 11

As it turned out, several quite different skills were required to
turn suspicions of data fitting, or tuning, into statistical proof. Some
were not part of the experise of the statisticians who had reviewed the
research for PNAS and Statistical Science. Math and computer skills were
required for the checking and the analysis of the quantitative parts of
the work. Hebrew and Talmudic expertise was required to evaluate the
choice of dates, appellations, and forms, and to uncover the unchosen
possibilities. That these different skills were brought to bear on the
codes is largely thanks to the persistent interest of Alec Gindis, a
Jerusalem-based businessman. Gindis has a summer house near David Kazhdan
in the Catskills, and had often discussed the codes with him. His
curiosity was aroused, but his religious sensibilities were offended. His
God, he felt, was not one to play around with primitive, childish codes.

Through Kazhdan, Gindis contacted Dror Bar-Natan, Dror Bar-Natan, a young
Israeli mathematician who had met Kazhdan while a post-doc at Harvard, to look into the
matter. Bar-Natan was eventually joined by his dpeartment colleague, Gil
Kalai. Through one of the Internet Torah Codes discussion groups, they
discovered and began a collaboration with Brendan McKay, a mathematician
from Australia's National University, with a previous history of debunking
numerological sci-fi. McKay had begun his own critical examination of the
codes, and was delighted to discover that he was not alone. In June 1997
McKay came to Jerusalem to meet both the advocates of the codes, and the
local skeptics. The meeting, which had been set months in advance,
happened to right after the publication of Drosnin's book. Thus McKay, a
much sought-after commentator on the codes, happened to be interviewed in
Israel for TV stations the world over.

One such interview was taped at the Western Wall by Italian TV.
Drosnin, in Rome, was confronted by McKay, in Jerusalem. McKay countered
Drosnin's letter arrays with letter arrays of his own. Drosnin relates
how he had found in the book of Isaiah (which Witztum and Rips, ironically
enough, had used as a control text, namely one which should not have
codes) a letter array relating to the 1994 collision of the Shoemaker-Levi
comet with the planet Jupiter, and also including the collision date.
McKay noted that Drosnin, perhaps unaware that Jewish dates change at
sundown rather than at midnight, had an incorrect date. To the glee of
the studio audience, McKay produced his own letter array of the cosmic
explosion, but with the correct date! The coup de grace was that McKay's
array was found in the Hebrew translation of War and Peace...

In a Newsweek interview, 13 Drosnin had stated: "When my critics
find a message about the assassination of a prime minister encrypted in
Moby Dick, I'll believe them". Not one to shirk a challenge, McKay found
a letter array in Moby Dick, containing an ELS message "predicting" the
murder of Drosnin himself. He also found arrays "predicting" many of the
major assassinations of the century, includingTrotsky, John Kennedy,
Robert Kennedy, and the Reverend King's (Figure 1). In spite of notable
differences between the two languages, these arrays (in English) closely
mimic the Rabin assassination array (in Hebrew), allowing the English
speaking reader to appreciate how tenous these predictions are. Of
course, McKay's discoveries in Moby Dick, like Drosnin's in the Torah,
don't really "predict" anything specific.
Figure 3 shows an array from Moby Dick relating to Princess Diana's fatal
car accident.

Figure 3.
Lady Diana, a member of the British royal family, died in a car accident

together with her boyfriend Dodi and the driver Henri Paul. 14

Far from being frivolous, McKay's letter sequences go to the heart
of the matter by showing that anecdotal messages like those which Drosnin
and Witztum find in the Bible can be found anywhere. But can even the
famous rabbis experiment be replicated anywhere? We already know that
letter for letter, the rabbis list failed in War and Peace. But could
success be achieved within the "wiggle room" which the choice of names
allowed?

To demonstrate this, McKay and Bar-Natan, with the scholarly help
of some others, constructed a list whose "performance" in War and Peace
matches or surpasses the performance of the original list in Genesis. The
criteria for choosing the rabbis, the dates used, letter for letter, the
various calculations -- all are the same. Only the list of chosen names
and appellations have been slightly altered, tuned explicitly to work well
on War and Peace. This was done by systematically writing down many
permissible names, appellations and spellings of some rabbi, and
preferring those that are felicitous for War and Peace to those that are
not. Remarkably, the adjusted list overlaps the original list by about
80%. Some of the changes are as trivial as changing Horovitz to Horowitz
(in the case of a rabbi documented to have been spelled both ways). Far
from being, or claiming to be, perfect, the list nonetheless is as
historically accurate and internally consistent as the original list.

As a complement to this work, McKay and Bar-Natan also checked how
Witztum and Rips' lists, letter for letter, worked on the four other books
of the Pentateuch (Exodus, Leviticus, Numbers, and Deuteronomy), all five
of which together comprise the holy Torah. In not a single book did they
find the slightest statistical evidence for anything that could not be
attributed to mere chance. A title for their results could very well
mimic the Statistical Science title: Equidistant letter sequences in the
book of War and Peace.

In 1999, Statistical Science published a paper by McKay,
Bar-Natan, Bar-Hillel and Kalai called Solving the Bible Code Puzzle. 15
It contains details of the War and Peace tuned experiment described above,
as well as much other material, some highly technical. It underwent the
same rigorous review process that the original work had undergone, in part
by the same experts. It is an embarrassment, at best, to that work.
Engaging the services of a law firm, Witztum and Rips sought to halt
publication of the critical paper, by threatening Statisitcal Science with
a libel suit if they published it. In response, the 1994 editor of
Statistical Science was invited to write a preface to the article. Kass
wrote that "there is good reason to think that the particular forms of
words [Witztum and Rips] chose effectively "tuned" their method to their
data, thus invalidating their statistical test", and concluded that "it
indeed appears ... that the puzzle has been solved" 16 (p. 149). The
present editor, Prof. Leon Gleser of the University of Pittsburgh,
accompanied the publication of the article with an unprecedented press
release. In the scientific world, if not in the religious one, it is safe
to say that the Bible code has been laid to rest.

In the aftermath, one might ask how so many prominent
mathematicians apparently come so close to accepting the genuineness of
Codes? Many people believe mathematics to be the very embodiment of
rigor, logic, precision and sheer brainpower. In fact, however,
mathematics demands less common sense and street-smarts from its
practitioners regarding the possibility of bias, fraud, or evasiveness
than any other science. In mathematics, a written proof is wholly
self-contained. Either it can be confired, or it cannot. It is
irrelevant how the proof came about, who the mathematician is being paid
by, and whether there is anything that is not being disclosed. Nothing
need be taken on faith, and a gullible mathematician is not at a
disadvantage.

In contrast, in all empirical sciences, everything about the
reported results depends crucially on the manner in which they were
obtained: the protocol, the methodology, the tools, the assumptions, the
measurement devices, even the motivations. Without some degree of trust,
nothing in empirical science can be believed.

Of the four mathematicians who endorsed Witztum's book, not one is
willing to speak out today in support of the codes. When The Discovery
Channel recently produced a program on the codes, they could not find a
single academic of any discipline who was willing to defend the codes. As
to statisticians -- not even the referees who finally endorsed the article
for publication were ever swayed by it. They just gave up on finding the
flaw, or, more accurately, on being able to prove it. Kass, who had made
the editorial decision to publish Witztum and Rips' work, said in an
interview following the publication of Drosnin's book: "Rips is not a
statistician. They wouldn't be doing this if they were statisticians.
Statisticians are professional skeptics. I'd be very surprised to see any
statistician believe any of this." 17

Einstein is quoted as having said: "God is subtle, but He is not
malicious". That is to say, the physical world is difficult to
understand, but it is not deliberately evasive. That is why natural
scientists, too, are often ill prepared to consider deception in the
phenomena they study. In contrast, people, and their creations, are often
deliberately evasive, misleading, and deceptive. They sometimes go to
great lengths to avoid being found out. Hence, the people best equipped
to detect deception are often those who practice it: magicians,
politicians, and used-car salesmen.

The well-known Argument from the Design takes the facts of the
world being so orderly, and its creatures so purposeful, to prove the
existence of a divine designer. The Torah code is, in fact, a similar
argument for the existence of God. It is a "proof" meant to convince
skeptics, who doubt the existence of God, and to strengthen the believers
in their belief. By testing features of the text that are supposedly
explainable neither by human design nor by chance, it begs the inference
that their only explanation is divine authorship of the text. It takes as
powerful a theory as the theory of evolution to show how, given world
enough and time, the universe could be an outcome of mere chance
processes. It takes a simple computer program to show that the codes,
those pretty letter arrays with the ELSs relating to future events in
them, are likewise the outcomes of chance processes. Sadly, it is not the
codes themselves, but rather the alleged "proof" that the codes cannot be
due to chance, that nec

essitates the inferring of design -- an all too
human design.

Aumann has stated, on more than one occasion, that the codes, if
they are genuine, are the most important religious event since the Torah
was given to Moses on Mt. Sinai. Far from being the discovery of the
millenium, however, the codes may well be the folly, if not the hoax, of
the decade.

Margaliot, M. (1961) Encyclopedia of Great Men in Israel: A
Bibliographical Dictionary of Jewish Sages and Scholars from the
9th Century to the End of the 18th Century, vols. 1-4. Joshua Chachik,
Tel Aviv (in Hebrew).

Tractate Yebamoth 47b.

Wall Street Journal, Monday, November 11, 1996.

Witztum, D. (1989) The Added Dimension: On Two-Dimensional Writing in
the Torah. Self-published in Israel in the Hebrew language.